数据集的维数有一个词吗？

Question

I have some code that generates some code, and I want to store the number of dimensions of the resulting data structure in a variable. I'm looking for the right name for this variable. For example, int should have the value 0, List<int> should have the value 1, List<List<int>> should have the value 2, and so on.

Is there a word from set theory or otherwise that describes this number? (At first I thought it was cardinality but apparently that's the size of a set, not the nested-ness of the set....)

Answer 1

The word you are looking for, would seem to be rank

In computer programming, rank with no further specifications is usually a synonym for (or refers to) "number of dimensions"; thus, a bi-dimensional array has rank two, a three-dimensional array has rank three and so on. Strictly, no formal definition can be provided which applies to every programming language, since each of them has its own concepts, semantics and terminology; the term may not even be applicable or, to the contrary, applied with a very specific meaning in the context of a given language.

The same term is also used in linear algebra :

In linear algebra, the rank of a matrix A is the size of the largest collection of linearly independent columns of A (the column rank) or the size of the largest collection of linearly independent rows of A (the row rank). For every matrix, the column rank is equal to the row rank. It is a measure of the "nondegenerateness" of the system of linear equations and linear transformation encoded by A. There are multiple equivalent definitions of rank. A matrix's rank is one of its most fundamental characteristics.

Also refer to this discussion on the definition of rank as related to sets from the maths stackexchange.

Finally this is how OPs employer names it for arrays :D